Without his glasses, Isaac can see objects clearly only if they are less than 4.2 m from his eyes. What focal length glasses worn 2.2 cm from his eyes will allow Isaac to see distant objects clearly?
Our book says to convert the cm to m and subtract the two numbers-
4.2 - 0.022 = 4.178m. We submit our answers on-line though, and this answer was incorrect. What am I doing wrong?
the answer should be negative
The approach mentioned in your book is not correct because it assumes that the glasses will bring the object into focus at a distance of 4.178 m from the eyes, which is not what is required in this case.
To find the correct focal length glasses, we need to consider the condition for clear vision without glasses. According to the given information, Isaac can see objects clearly if they are less than 4.2 m from his eyes. This means his near point without glasses (NPD) is 4.2 m.
The focal length of the glasses needed can be determined using the formula for the near point of a person wearing glasses:
NPD with glasses = 1 / (focal length of the glasses) - 1 / (NPD without glasses)
Plugging in the given values:
4.2 m = 1 / (f) - 1 / (4.178 m)
To solve for the focal length (f) in meters, we can rearrange the equation as follows:
1 / (f) = 1 / (4.178 m) + 1 / (4.2 m)
1 / (f) = (4.2 + 4.178) / ((4.178)(4.2))
1 / (f) = 8.378 / (17.53036 m^2)
f = (17.53036 m^2) / 8.378
f ≈ 2.092 m
Therefore, the focal length of the glasses Isaac needs to see distant objects clearly is approximately 2.092 meters.
Make sure to double-check your calculations and ensure correct unit conversions to avoid any errors when submitting your answer online.